What is expand 5/(x+1)+((3x-1))/(x^2+x+1) ?

The solution to expand 5/(x+1)+((3x-1))/(x^2+x+1) is (8x^2+7x+4)/(x^3+2x^2+2x+1)

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expand 5/(x+1)+((3x-1))/(x^2+x+1)

expand

\frac{5}{x + 1} + \frac{( 3 x - 1 )}{x ^{2} + x + 1}

\frac{8 x ^{2} + 7 x + 4}{x ^{3} + 2 x ^{2} + 2 x + 1}

Solution steps

\frac{5}{x + 1} + \frac{3 x - 1}{x ^{2} + x + 1}

Least Common Multiplier of

x + 1, x^{2} + x + 1 : (x + 1) (x^{2} + x + 1)

Adjust Fractions based on the LCM

= \frac{5 ( x ^{2} + x + 1 )}{( x + 1 ) ( x ^{2} + x + 1 )} + \frac{( 3 x - 1 ) ( x + 1 )}{( x ^{2} + x + 1 ) ( x + 1 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 ( x ^{2} + x + 1 ) + ( 3 x - 1 ) ( x + 1 )}{( x + 1 ) ( x ^{2} + x + 1 )}

Expand

(x + 1) (x^{2} + x + 1) : x^{3} + 2 x^{2} + 2 x + 1

= \frac{5 ( x ^{2} + x + 1 ) + ( 3 x - 1 ) ( x + 1 )}{x ^{3} + 2 x ^{2} + 2 x + 1}

Expand

5 (x^{2} + x + 1) + (3 x - 1) (x + 1) : 8 x^{2} + 7 x + 4

= \frac{8 x ^{2} + 7 x + 4}{x ^{3} + 2 x ^{2} + 2 x + 1}

(- e^{2 t} sin (t) + e^{2 t} cos (t))^{2}

\frac{3 ( x ^{2} - 9 x + 20 )}{2}

(x^{2} - 5 e x + 3) (x^{3} + 2 x + 1)

1 + (\frac{( x ^{4} + 9 )}{( 18 x )})^{2}

(bi + c j + d k)^{2}

What is expand 5/(x+1)+((3x-1))/(x^2+x+1) ?
The solution to expand 5/(x+1)+((3x-1))/(x^2+x+1) is (8x^2+7x+4)/(x^3+2x^2+2x+1)